Question

Suppose f(x) = x^3 +3. Find the graph of f(2/3x)

Answer 1

First, when we have a function f(x), an horizontal dilation of scale factor k, is written as:

g(x) = f(x/k)

Then f((2/3)*x) is an horizontal dilation of scale factor 3/2 of the function f(x).

(The graph will be a little bit wider than the graph of f(x))

Also, knowing that f(x) = x^3 + 3

Then:

f((2/3)*x) = ( (2/3)*x)^3 + 3

= (8/27)*x^3 + 3

And the graph of this function is shown below: